The present disclosure relates generally to measurement techniques, and more specifically, to a Hall measurement system with a rotary magnet.
Hall measurement is a characterization technique that may be used in a variety of applications, such as semiconductor and solid state device research. Hall measurement enables measurement of a free carrier density, which may yield carrier mobility when considered together with a resistivity measurement. The so-called Hall effect occurs when a current is passed through a material with an applied perpendicular magnetic field, such that a Hall voltage VH is generated, as provided in equation #1 as follows:VH=BI/nde  Eq. #1
In equation #1 above, B is the magnetic field, I is the electric current passing through the sample, n is the free carrier density, d is the sample thickness and e is the charge of an electron.
A figure of merit in the Hall measurement is the Hall angle φ, whose tangent is defined as the ratio between the Hall or transverse resistance (Rxy) and the longitudinal resistance (Rxx). The tangent of this Hall angle, in the case of a square sample, may be given by equation #2 as follows:tan φ=Rxy/Rxx=Bμ  Eq. #2
In equation #2 above, μ is the mobility of the majority carrier.
A good or quality Hall measurement requires a sufficiently large Hall angle or tan φ on the order of unity. Based on equation #2, a problem may arise when a sample has poor mobility (e.g., μ<<1 cm2/Vs) or the magnetic field that is available is limited (e.g., B<<0.1 Tesla). Furthermore, based on equation #1, samples with a very high carrier density n may also cause a small Hall voltage VH. Some measurement environments, such as low temperature measurement, dictate the use of a very small excitation current I, thus resulting in a small Hall voltage VH. In such situations, a DC magnetic field Hall measurement may yield a small Hall voltage VH buried within a large DC voltage offset due to sample geometrical asymmetry. The asymmetry may cause a mixing of the Hall or transverse resistance (Rxy) and the longitudinal resistance (Rxx).